DG-GAN: A High Quality Defect Image Generation Method for Defect Detection

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. 2023 Jun 26;23(13):5922. doi: 10.3390/s23135922

Algorithm 1 Algorithm training of DG-GAN model.

$θ_{C}, θ_{G}, θ_{D 1_{f}}, θ_{D 2_{f}}, θ_{D 1_{i}}, θ_{D 2 i} \Leftarrow$ Initialize the network parameters
Repeat
Real defect-free image sample $f \in P_{r} (f)$
Real defect image sample $i \in P_{r} (i)$
Obtain generated defect-free image $\hat{f}$ where $\hat{f} = C (i)$
Update discriminator $D 1_{f}$ ’s parameters to maxmize:
$\nabla θ_{D 1_{f}} E_{f \in P_{r} (f)} [l o g D 1_{f} (f)] + E_{i \in P_{r} (i)} [l o g (1 - D 1_{f} (\hat{f}))]$
Update discriminator $D 2_{f}$ ’s parameters to maxmize:
$\nabla θ_{D 2_{f}} E_{i \in P_{r} (i)} [l o g D 2_{f} (\hat{f})] + E_{f \in P_{r} (f)} [l o g (1 - D 2_{f} (f))]$
Update generator F’s parameters to minimize:
$\nabla θ_{F} E_{i \in P_{r} (i)} [l o g D 1_{f} (\hat{f})] + E_{i \in P_{r} (i)} [l o g (1 - D 2_{f} (C (i)))] + ∥G (\hat{f}) - i∥$
Obtain generated defect image $\hat{i}$ where $\hat{i} = G (f)$
Update discriminator $D 1_{i}$ ’s parameters to maxmize:
$\nabla θ_{D 1_{i}} E_{i \in P_{r} (i)} [l o g D 1_{i} (i)] + E_{f \in P_{r} (f)} [l o g (1 - D 1_{i} (\hat{i}))]$
Update discriminator $D 2_{i}$ ’s parameters to maxmize:
$\nabla θ_{D 2_{i}} E_{f \in P_{r} (f)} [l o g D 2_{i} (\hat{i})] + E_{i \in P_{r} (i)} [l o g (1 - D 2_{i} (i))]$
Update generator G’s parameters to minimize:
$\nabla θ_{G} E_{f \in P_{r} (f)} [l o g D 1_{i} (\hat{i})] + E_{f \in P_{r} (f)} [l o g (1 - D 2_{i} (G (i)))] + ∥C (\hat{i}) - f∥$
Until convergence
Real defect-free image sample $f \in P_{r} (f)$
Obtain generated defect image $\hat{i}$ where $\hat{i} = G (f)$
Return $\hat{i}$